Minimum Path Sum
/**
* Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.
* Note: You can only move either down or right at any point in time.
*/
public class Solution {
public int minPathSum(int[][] grid) {
int[][] path = new int[grid.length][grid[0].length];
path[0][0] = grid[0][0];
// Initialize the border: Up and left
for(int i = 1; i < grid.length; i++){
path[i][0] = path[i - 1][0] + grid[i][0];
}
for(int i = 1; i < grid[0].length; i++){
path[0][i] = path[0][i - 1] + grid[0][i];
}
// walk the grid
for(int i = 1; i < grid.length; i++){
for(int j = 1; j < grid[0].length; j++){
path[i][j] = Math.min(path[i - 1][j], path[i][j - 1]) + grid[i][j];
}
}
return path[grid.length - 1][grid[0].length - 1];
}
}